Recent questions in Differential equations

Solve differential equation $$t^2dy= (8ln^2t-ty)dt$$

Laplace transform

Solve the following initial value problems using Laplace Transforms: $$\displaystyle\frac{{{d}^{2}{y}}}{{{\left.{d}{x}\right.}^{2}}}+{25}{y}={t}$$ $$y(0)=0$$ $$y'(0)=0.04$$

Laplace transform

How many poles does the Laplace Transform of a square wave have? a) 0 b) 1 c) 2 d) Infinitely Manhy

Differential equations

Solve the linear equations by considering y as a function of x, that is, y = y(x). $$\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}-{y}={4}{e}^{x},{y}{\left({0}\right)}={4}$$

Laplace transform

Use properties of the Laplace transform to answer the following (a) If $$f(t)=(t+5)^2+t^2e^{5t}$$, find the Laplace transform,$$L[f(t)] = F(s)$$. (b) If $$f(t) = 2e^{-t}\cos(3t+\frac{\pi}{4})$$, find the Laplace transform, $$L[f(t)] = F(s)$$. HINT: $$\cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha) \sin(\beta)$$ (c) If $$F(s) = \frac{7s^2-37s+64}{s(s^2-8s+16)}$$ find the inverse Laplace transform, $$L^{-1}|F(s)| = f(t)$$ (d) If $$F(s) = e^{-7s}(\frac{1}{s}+\frac{s}{s^2+1})$$ , find the inverse Laplace transform, $$L^{-1}[F(s)] = f(t)$$

Laplace transform

Solve no.4 inverse laplace $$L^{-1}\left\{s \ln\left(\frac{s}{\sqrt{s^2+1}}\right)+\cot^{-1s}\right\}$$

Differential equations

Give the correct answer and solve the given equation: $$\displaystyle{y}\ \text{ - 4y}+{3}{y}={x},{y}_{{1}}={e}^{x}$$

Laplace transform

Solve the linear equations by considering y as a function of x, that is, y = y(x). $$\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}+{\left(\frac{1}{{x}}\right)}{y}={x}$$

Laplace transform

determine the inverse Laplace transform of F. $$F(s)=\frac{e^{-2s}}{(s-3)^3}$$

Laplace transform